An election puzzle

John Jackson and Jack Johnson were going head to head in a mayoral race. Ultimately John Jackson obtained 300 votes and Jack Johnson obtained 200 votes. While counting the votes they announced after each vote what the current results were. For example after they counted the first vote they announced something like:

“John Jackson: 1; Jack Johnson: 0”

and then after the second vote

“John Jackson: 1; Jack Johnson: 1”

and so on until they finally counted the last vote and announced

“John Jackson: 300; Jack Johnson: 200”

Not counting the very beginning when the results were “John: 0; Jack: 0” - What is the probability that at some point during the counting the result was a tie?

There is a nice solution to this that I will give in my next post. Try to figure it out in the meantime!